2009 AMC 10 B, Problem #4—2009 AMC 12 B, Problem #4—“Each triangle has leg length12·(25-15) = 5meters.”SolutionAnswer (C):Each triangle has leg length12·(25-15) = 5meters andarea12·52=252square meters. Thus the flower beds have a total area of25 square meters. The entire yard has length 25 and width 5, so its areais 125. The fraction of the yard occupied by the flower beds is25125=15.Difficulty:Medium-easyNCTM Standard:Geometry Standard: analyze properties and determine attributes of two- andthree-dimensional objects.Mathworld.com Classification:Geometry>Plane Geometry>Miscellaneous Plane Geometry>Area

Twenty percent less than 60 is one-third more thanwhat number?
Difficulty:MediumNCTM Standard:Algebra Standard: understand the meaning of equivalent forms of expressions,equations, inequalities, and relations.Mathworld.com Classification:Number Theory>Arithmetic>Fractions>Fraction

Kiana has two older twin brothers.The product oftheir three ages is 128. What is the sum of their threeages?(A)10(B)12(C)16(D)18(E)242009 AMC 10 B, Problem #6—2009 AMC 12 B, Problem #5—“Note that128 = 27.”SolutionAnswer (D):The age of each person is a factor of128 = 27. So the twinscould be20= 1,21= 2,22= 4,23= 8years of age and, consequently,Kiana could be12812= 128,12822= 32,12842= 8, or12882= 2years old,respectively. Because Kiana is younger than her brothers, she must be 2years old. The sum of their ages is2 + 8 + 8 = 18.Difficulty:Medium-easyNCTM Standard:Algebra Standard: identify essential quantitative relationships in a situationand determine the class or classes of functions that might model the relationships.Mathworld.com Classification: NEED CATEGORY!

By inserting parentheses, it is possible to give theexpression2×3 + 4×5several values.How many different values can beobtained?(A)2(B)3(C)4(D)5(E)62009 AMC 10 B, Problem #7—2009 AMC 12 B, Problem #6—“The three operations can be performed in any of3! = 6orders.”
Difficulty:MediumNCTM Standard:Number and Operations Standard:understand meanings of operations andhow they relate to one another.Mathworld.com Classification: NEED CATEGORY! Which recreational math was it?

In a certain year the price of gasoline rose by 20%during January, fell by 20% during February, rose by25% during March, and fell byx% during April. Theprice of gasoline at the end of April was the same as ithad been at the beginning of January. To the nearestinteger, what isx?
2009 AMC 10 B, Problem #8
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